I Two numerical questions about inflation and the flatness problem

Good day to you all
I just started studying cosmology recently using several book and especially using
TASI Lectures on Inflation(https://arxiv.org/abs/0907.5424)

On page 25 the fine tuning problem of the flatness is introduced with conditions as
|Ω(BBN)-1|≤ ο(10-16)
|Ω(GUT)-1|≤ ο(10-55)
|Ω(pl)-1|≤ ο(10-61)
My first question is how to derive this condition

The second would be page 34 where the number of inflationary e-folds were introduced and simply put that it must be more than 60 to solve the flatness and horizon problems
I was unable to derive this also

Furthermore I suppose that these conditions are derived from observations
It would be great if I could calculate these conditions a bit more exact using recent data...

Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?